Parameter identification of constrained data by a new class of rational fractal function
S.K. Katiyar, A.K.B. Chand, S. Jha
1Indian Institute of Technology Madras, Chennai, India
2Indian Institute of Technology Madras, Ченнаи, Индия
Keywords: iterated function system, fractal interpolation functions, rational cubic fractal functions, rational cubic interpolation, constrained interpolation, positivity
Abstract
This paper sets a theoretical foundation for applications of fractal interpolation functions (FIFs). We construct rational cubic spline FIFs (RCSFIFs) with a quadratic denominator involving two shape parameters. The elements of the iterated function system (IFS) in each subinterval are identified befittingly so that the graph of the resulting C1-RCSFIF lies within a prescribed rectangle. These parameters include, in particular, conditions on the positivity of the C1-RCSFIF. The problem of visualization of constrained data is also addressed when the data is lying above a straight line, the proposed fractal curve is required to lie on the same side of the line. We illustrate our interpolation scheme with some numerical examples.
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